Amenable actions of inverse semigroups

Abstract

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse semigroup $S$, the action of $S$ on its spectrum is amenable if and only if every action of $S$ is amenable.

9 pages. Version 2 adds references and fixes typos. This version to appear in Ergodic Theory and Dynamical Systems

References in corpus (1)

• A non-amenable groupoid whose maximal and reduced $C^{\ast }$-algebras are the same

Cited by in corpus (2)

• The uniform Roe algebra of an inverse semigroup
• Amenability and paradoxicality in semigroups and C*-algebras